NOTE Need to examine all MIs for strict model and drop items accordingly.

Creating factor-item mapping

As part of this process, outputting the alpha coefficients.

## **Wave 1**
##          aspfin    bfa_mt bfas_ac   bfas_ap   bfas_ci   bfas_co   bfas_ea
## alpha 0.8007216 0.7922283 0.88408 0.7814323 0.8559713 0.7748649 0.8882828
##         bfas_ee   bfas_nv  bfas_nv9   bfas_nw   bfas_oi   bfas_oo
## alpha 0.8547331 0.9113937 0.9010348 0.8781388 0.8287349 0.7899743
##           bfi_a    bfi_a6    bfi_c bfi_d_scale     bfi_e   bfi_hp8
## alpha 0.8009146 0.7908462 0.819993   0.7966031 0.8749101 0.6762593
##           bfi_n     bfi_o bfi_s_scale   hrz_col  hrz_ind       usi
## alpha 0.8582059 0.7898225   0.7969331 0.7126198 0.550577 0.6732525
##         vrt_col   vrt_ind
## alpha 0.6743606 0.6523363
##             mvi
## alpha 0.6078291
## **Wave 2**
##          aspfin    bfa_mt   bfas_ac   bfas_ap   bfas_ci   bfas_co
## alpha 0.8252445 0.7796828 0.8829338 0.7785236 0.8492025 0.7839002
##         bfas_ea   bfas_ee   bfas_nv  bfas_nv9   bfas_nw   bfas_oi
## alpha 0.8761572 0.8590842 0.8972032 0.8854566 0.8698163 0.8153715
##         bfas_oo     bfi_a    bfi_a6     bfi_c bfi_d_scale     bfi_e
## alpha 0.7970451 0.7962796 0.7961057 0.8071378   0.7858279 0.8664445
##         bfi_hp8     bfi_n     bfi_o bfi_s_scale   hrz_col   hrz_ind
## alpha 0.6848438 0.8587661 0.7966047   0.7848152 0.6932522 0.5938064
##             usi   vrt_col   vrt_ind
## alpha 0.6929115 0.7115297 0.6393136
##             mvi
## alpha 0.6322902
## **Wave 3**
##          aspfin    bfa_mt   bfas_ac   bfas_ap   bfas_ci   bfas_co
## alpha 0.8338066 0.8026428 0.8862414 0.7768773 0.8492295 0.7774236
##         bfas_ea   bfas_ee   bfas_nv  bfas_nv9   bfas_nw   bfas_oi
## alpha 0.8819575 0.8616749 0.9007862 0.8903142 0.8817477 0.8376555
##         bfas_oo    bfi_a    bfi_a6     bfi_c bfi_d_scale     bfi_e
## alpha 0.8028977 0.803164 0.7982502 0.8213291   0.7909743 0.8728148
##         bfi_hp8     bfi_n     bfi_o bfi_s_scale   hrz_col   hrz_ind
## alpha 0.6738761 0.8582405 0.8133423   0.7918976 0.7079314 0.5391312
##             usi   vrt_col   vrt_ind
## alpha 0.6881401 0.6990938 0.6752587
##             mvi
## alpha 0.6560747
## **Wave 4**
##          aspfin    bfa_mt   bfas_ac   bfas_ap   bfas_ci   bfas_co  bfas_ea
## alpha 0.8347909 0.7945824 0.8874039 0.7633623 0.8518579 0.7937478 0.881371
##         bfas_ee   bfas_nv  bfas_nv9   bfas_nw   bfas_oi   bfas_oo
## alpha 0.8705236 0.9131165 0.9049279 0.8847419 0.8329141 0.8025353
##           bfi_a    bfi_a6     bfi_c bfi_d_scale     bfi_e  bfi_hp8
## alpha 0.8117976 0.8028806 0.8218647   0.8056326 0.8749207 0.665913
##           bfi_n     bfi_o bfi_s_scale   hrz_col   hrz_ind       usi
## alpha 0.8745566 0.8100603   0.7937251 0.7041649 0.5645062 0.6852414
##         vrt_col   vrt_ind
## alpha 0.7266396 0.6538177
##             mvi
## alpha 0.6034461

Generate lavaan syntax

Note: I use the identification strategy recommended by Widman, Ferrer, and Conger (2010) and set the intercept for the Wave 1 latent variable to 0, and the variance of the Wave 1 latent variable to 1 for each group.

This is an example of the measurement model diagram, using Horizontal Collectivism, for one group demonstrating constraints for the strict measurement invariance model. Paths with the same label are constrained to have the same path weight, and in the strict invariance model, all labeled path weights must be the same for each decade group. The residual covariances are an exception: the constraint imposed is that residual covariance is the same across the same time-lag, for the same indicator (so e.g., cov(aind9, bind9) = cov(bind9, cind9), and cov(aind9, cind9) = cov(bind9, dind9)), but these are not constrained to be the same across group. Since this constraint is imposed in every factorial invariance model tested, it does not affect the fit comparisons.

## hrz_col_W1 ~ 0*1
## hrz_col_W1 ~~ 1*hrz_col_W1
## hrz_col_W1 =~ c(L1, L1, L1, L1)*aind9 + c(L2, L2, L2, L2)*aind10 + c(L3, L3, L3, L3)*aind11 + c(L4, L4, L4, L4)*aind12
## hrz_col_W2 =~ c(L1, L1, L1, L1)*bind9 + c(L2, L2, L2, L2)*bind10 + c(L3, L3, L3, L3)*bind11 + c(L4, L4, L4, L4)*bind12
## hrz_col_W3 =~ c(L1, L1, L1, L1)*cind9 + c(L2, L2, L2, L2)*cind10 + c(L3, L3, L3, L3)*cind11 + c(L4, L4, L4, L4)*cind12
## hrz_col_W4 =~ c(L1, L1, L1, L1)*dind9 + c(L2, L2, L2, L2)*dind10 + c(L3, L3, L3, L3)*dind11 + c(L4, L4, L4, L4)*dind12
## 
## #---
## 
## aind9 ~ c(int_1, int_1, int_1, int_1)*1
## bind9 ~ c(int_1, int_1, int_1, int_1)*1
## cind9 ~ c(int_1, int_1, int_1, int_1)*1
## dind9 ~ c(int_1, int_1, int_1, int_1)*1
## 
## aind10 ~ c(int_2, int_2, int_2, int_2)*1
## bind10 ~ c(int_2, int_2, int_2, int_2)*1
## cind10 ~ c(int_2, int_2, int_2, int_2)*1
## dind10 ~ c(int_2, int_2, int_2, int_2)*1
## 
## aind11 ~ c(int_3, int_3, int_3, int_3)*1
## bind11 ~ c(int_3, int_3, int_3, int_3)*1
## cind11 ~ c(int_3, int_3, int_3, int_3)*1
## dind11 ~ c(int_3, int_3, int_3, int_3)*1
## 
## aind12 ~ c(int_4, int_4, int_4, int_4)*1
## bind12 ~ c(int_4, int_4, int_4, int_4)*1
## cind12 ~ c(int_4, int_4, int_4, int_4)*1
## dind12 ~ c(int_4, int_4, int_4, int_4)*1
## 
## #---
## 
## aind9 ~~ c(v_1, v_1, v_1, v_1)*aind9
## bind9 ~~ c(v_1, v_1, v_1, v_1)*bind9
## cind9 ~~ c(v_1, v_1, v_1, v_1)*cind9
## dind9 ~~ c(v_1, v_1, v_1, v_1)*dind9
## 
## aind10 ~~ c(v_2, v_2, v_2, v_2)*aind10
## bind10 ~~ c(v_2, v_2, v_2, v_2)*bind10
## cind10 ~~ c(v_2, v_2, v_2, v_2)*cind10
## dind10 ~~ c(v_2, v_2, v_2, v_2)*dind10
## 
## aind11 ~~ c(v_3, v_3, v_3, v_3)*aind11
## bind11 ~~ c(v_3, v_3, v_3, v_3)*bind11
## cind11 ~~ c(v_3, v_3, v_3, v_3)*cind11
## dind11 ~~ c(v_3, v_3, v_3, v_3)*dind11
## 
## aind12 ~~ c(v_4, v_4, v_4, v_4)*aind12
## bind12 ~~ c(v_4, v_4, v_4, v_4)*bind12
## cind12 ~~ c(v_4, v_4, v_4, v_4)*cind12
## dind12 ~~ c(v_4, v_4, v_4, v_4)*dind12
## 
## #---
## 
## aind9 ~~ bind9
## aind9 ~~ cind9
## aind9 ~~ dind9
## bind9 ~~ cind9
## bind9 ~~ dind9
## cind9 ~~ dind9
## 
## aind10 ~~ bind10
## aind10 ~~ cind10
## aind10 ~~ dind10
## bind10 ~~ cind10
## bind10 ~~ dind10
## cind10 ~~ dind10
## 
## aind11 ~~ bind11
## aind11 ~~ cind11
## aind11 ~~ dind11
## bind11 ~~ cind11
## bind11 ~~ dind11
## cind11 ~~ dind11
## 
## aind12 ~~ bind12
## aind12 ~~ cind12
## aind12 ~~ dind12
## bind12 ~~ cind12
## bind12 ~~ dind12
## cind12 ~~ dind12

Results

MFI, CFI & *IC

To determine the invariance of measurement over groups, we can examine the \(\chi^2\) test. But this is often an overly strict test with a large sample size. Relative change in AIC and BIC (with lower values, and negative changes, being better) help guide interpretation by incorporating information about the number of parameters (AIC, BIC) and sample size (BIC). Kang, McNeish, & Hancock (2016) recommend using McDonald’s non-centrality parameter (McDonald, 1989) because it is not influenced by complexity, sample size, or measurement quality. Their simulation study indicates that under the null of no difference in model fit, a difference in the MFI, \(\Delta\text{MFI}\), of < -.007 occurs in fewer than 5% of cases, and < -.01 in less that 1% of cases. They also caution against using cutoffs.

Note: The baseline model adds to the strict longitudinal invariance model the additional constraint that covariance among residuals for the same item with the same lag distance must be the same.

Financial Aspirations
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 798 536 0.973 0.860 0.048 [0.041, 0.054]
2 long_metric 864 584 -30.4 -259.1 0.971 -0.002 0.851 -0.009 0.047 [0.040, 0.054]
3 long_strong 930 632 -29.3 -258.0 0.969 -0.002 0.842 -0.009 0.047 [0.040, 0.053]
4 long_strict 1015 692 -35.4 -321.2 0.966 -0.003 0.830 -0.012 -0.030 0.046 [0.040, 0.052]
5 metric 1039 707 -5.8 -77.3 0.965 -0.001 0.825 -0.004 -0.025 0.047 [0.040, 0.053]
6 strong 1079 722 10.2 -61.3 0.963 -0.003 0.814 -0.012 -0.028 0.048 [0.042, 0.054]
7 strict 1109 737 -0.4 -71.9 0.961 -0.002 0.807 -0.007 -0.023 0.048 [0.042, 0.054]

Strong longitudnal invariance. Metric invariance between groups is well supported.

Materialism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained NA [NA, NA]
2 long_metric 1456 900 0.930 0.725 0.053 [0.048, 0.058]
3 long_strong 1542 960 -34.1 -320.0 0.927 -0.003 0.715 -0.011 0.053 [0.048, 0.058]
4 long_strict NA [NA, NA]
5 metric 1656 1050 0.924 0.705 -0.020 0.052 [0.047, 0.056]
6 strong 1711 1068 18.6 -67.2 0.920 -0.005 0.690 -0.015 -0.024 0.053 [0.048, 0.057]
7 strict 1751 1086 4.5 -81.2 0.917 -0.003 0.681 -0.009 0.053 [0.049, 0.058]

Possibly problematic. Unconstrained model does not converge. MFI may be too low for accurate model comparison.

Horizontal Collectivism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 427 296 0.973 0.927 0.045 [0.035, 0.054]
2 long_metric 480 332 -18.6 -190.1 0.969 -0.004 0.918 -0.009 0.045 [0.036, 0.054]
3 long_strong 553 368 0.4 -171.1 0.962 -0.008 0.899 -0.019 0.048 [0.040, 0.056]
4 long_strict 609 416 -40.1 -268.8 0.960 -0.002 0.895 -0.004 -0.032 0.046 [0.038, 0.054]
5 metric 641 428 8.0 -49.1 0.956 -0.004 0.884 -0.010 -0.033 0.048 [0.040, 0.055]
6 strong 712 440 47.0 -10.2 0.944 -0.012 0.855 -0.030 -0.044 0.053 [0.046, 0.061]
7 strict 755 452 19.5 -37.7 0.937 -0.007 0.839 -0.015 -0.055 0.056 [0.049, 0.063]

Longitudinal metric invariance is supported. Group metric invariance is on the recommended cutoff.

Horizontal Individualism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 474 296 0.942 0.902 0.053 [0.044, 0.061]
2 long_metric 507 332 -39.5 -211.0 0.944 0.001 0.904 0.002 0.049 [0.041, 0.058]
3 long_strong 551 368 -27.3 -198.8 0.941 -0.003 0.900 -0.005 0.048 [0.039, 0.056]
4 long_strict 616 416 -31.0 -259.7 0.935 -0.005 0.891 -0.009 -0.011 0.047 [0.039, 0.055]
5 metric 634 428 -6.2 -63.4 0.933 -0.002 0.888 -0.003 -0.016 0.047 [0.039, 0.055]
6 strong 661 440 3.1 -54.1 0.928 -0.005 0.880 -0.008 -0.019 0.048 [0.040, 0.056]
7 strict 676 452 -9.6 -66.7 0.928 -0.001 0.879 -0.001 -0.012 0.048 [0.040, 0.055]

Invariant.

Mature Values Index
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 22996 8408 0.599 0.000 0.090 [0.088, 0.091]
2 long_metric 23260 8600 -119.9 -1034.6 0.597 -0.002 0.000 -0.000 0.089 [0.087, 0.090]
3 long_strong 23513 8792 -131.4 -1046.1 0.596 -0.002 0.000 -0.000 0.088 [0.087, 0.089]
4 long_strict 23793 8996 -128.2 -1100.0 0.594 -0.002 0.000 -0.000 -0.000 0.087 [0.086, 0.089]
5 metric 23861 9047 -33.8 -276.7 0.593 -0.000 0.000 -0.000 -0.000 0.087 [0.086, 0.088]
6 strong 24081 9098 117.9 -125.1 0.588 -0.005 0.000 -0.000 -0.000 0.087 [0.086, 0.089]
7 strict 24249 9149 66.0 -176.9 0.585 -0.003 0.000 -0.000 -0.000 0.087 [0.086, 0.089]

Possibly problematic.

Unmitigated Self-Interest
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained NA [NA, NA]
2 long_metric 1731 900 0.876 0.619 0.065 [0.061, 0.070]
3 long_strong 1814 960 -36.3 -322.1 0.872 -0.004 0.611 -0.008 0.064 [0.060, 0.069]
4 long_strict 1914 1032 -44.1 -387.1 0.868 -0.004 0.601 -0.010 0.063 [0.058, 0.067]
5 metric 1947 1050 -3.7 -89.5 0.866 -0.002 0.596 -0.005 -0.023 0.063 [0.058, 0.067]
6 strong 2015 1068 32.8 -52.9 0.858 -0.008 0.579 -0.017 -0.032 0.064 [0.060, 0.068]
7 strict 2083 1086 31.0 -54.7 0.851 -0.007 0.563 -0.016 -0.038 0.065 [0.061, 0.069]

The unconstrained model did not converge. Strict longitudinal invariance may be supported. Group metric invariance is supported, but not strong group invariance.

Vertical Collectivism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 352 296 0.988 0.968 0.029 [0.014, 0.041]
2 long_metric 376 332 -47.4 -218.9 0.991 0.002 0.975 0.006 0.025 [0.003, 0.037]
3 long_strong 413 368 -35.0 -206.5 0.990 -0.000 0.974 -0.001 0.024 [0.000, 0.035]
4 long_strict 473 416 -35.7 -264.3 0.988 -0.003 0.967 -0.007 -0.001 0.025 [0.009, 0.036]
5 metric 506 428 8.9 -48.3 0.983 -0.004 0.956 -0.012 -0.019 0.029 [0.017, 0.039]
6 strong 565 440 35.1 -22.1 0.973 -0.010 0.930 -0.026 -0.044 0.036 [0.027, 0.045]
7 strict 589 452 -0.8 -57.9 0.971 -0.002 0.924 -0.006 -0.043 0.037 [0.028, 0.046]

Longitudinal strict invariance is well supported. Group metric invariance is not supported.

Vertical Individualism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 343 296 0.989 0.973 0.027 [0.009, 0.039]
2 long_metric 380 332 -35.2 -206.7 0.989 -0.000 0.973 -0.000 0.026 [0.007, 0.037]
3 long_strong 413 368 -38.9 -210.4 0.990 0.001 0.974 0.002 0.024 [0.000, 0.035]
4 long_strict 468 416 -40.8 -269.5 0.988 -0.002 0.970 -0.004 -0.003 0.024 [0.006, 0.035]
5 metric 489 428 -3.6 -60.7 0.986 -0.002 0.966 -0.005 -0.007 0.026 [0.011, 0.036]
6 strong 550 440 37.2 -20.0 0.975 -0.011 0.938 -0.027 -0.036 0.034 [0.024, 0.043]
7 strict 563 452 -10.9 -68.1 0.975 -0.000 0.938 -0.001 -0.032 0.034 [0.024, 0.042]

Longitudinal strict invaraince is well supported. Group metric invariance is well supported.

.Conscientiousness
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 3379 2136 0.904 0.488 0.052 [0.048, 0.055]
2 long_metric 3481 2232 -89.9 -547.4 0.904 -0.000 0.487 -0.002 0.051 [0.048, 0.054]
3 long_strong 3576 2328 -96.9 -554.4 0.904 0.000 0.487 0.000 0.050 [0.046, 0.053]
4 long_strict 3733 2436 -58.6 -573.2 0.900 -0.004 0.473 -0.014 -0.015 0.050 [0.046, 0.053]
5 metric 3763 2463 -25.0 -153.6 0.900 -0.000 0.473 -0.001 -0.014 0.049 [0.046, 0.052]
6 strong 3845 2490 28.6 -100.0 0.895 -0.004 0.458 -0.015 -0.029 0.050 [0.047, 0.053]
7 strict 3938 2517 39.0 -89.6 0.890 -0.005 0.441 -0.017 -0.033 0.051 [0.048, 0.054]

.Agreeableness
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 3054 2136 0.925 0.589 0.045 [0.041, 0.048]
2 long_metric 3169 2232 -77.7 -535.2 0.924 -0.001 0.583 -0.006 0.044 [0.040, 0.047]
3 long_strong 3313 2328 -47.3 -504.7 0.920 -0.004 0.567 -0.016 0.044 [0.041, 0.048]
4 long_strict 3425 2436 -104.8 -619.4 0.919 -0.000 0.565 -0.001 -0.023 0.043 [0.040, 0.047]
5 metric 3459 2463 -19.7 -148.3 0.919 -0.001 0.563 -0.002 -0.020 0.043 [0.040, 0.047]
6 strong 3514 2490 0.8 -127.9 0.916 -0.002 0.554 -0.009 -0.012 0.044 [0.040, 0.047]
7 strict 3564 2517 -3.9 -132.6 0.915 -0.002 0.547 -0.007 -0.019 0.044 [0.040, 0.047]

.Neuroticism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 2504 1640 0.937 0.608 0.049 [0.045, 0.053]
2 long_metric 2592 1724 -79.6 -479.8 0.937 -0.000 0.606 -0.002 0.048 [0.044, 0.052]
3 long_strong 2703 1808 -57.2 -457.5 0.935 -0.002 0.597 -0.009 0.048 [0.044, 0.051]
4 long_strict 2799 1904 -96.5 -553.9 0.935 0.000 0.597 0.000 -0.011 0.047 [0.043, 0.050]
5 metric 2820 1928 -27.1 -141.5 0.935 0.000 0.598 0.001 -0.008 0.046 [0.042, 0.050]
6 strong 2880 1952 12.1 -102.2 0.933 -0.003 0.586 -0.012 -0.011 0.047 [0.043, 0.050]
7 strict 2918 1976 -9.7 -124.1 0.932 -0.001 0.581 -0.005 -0.016 0.047 [0.043, 0.050]

.Extraversion
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 2977 1640 0.921 0.463 0.061 [0.058, 0.065]
2 long_metric 3044 1724 -100.9 -501.2 0.922 0.001 0.467 0.005 0.059 [0.056, 0.063]
3 long_strong 3140 1808 -72.0 -472.2 0.921 -0.001 0.464 -0.003 0.058 [0.055, 0.062]
4 long_strict 3243 1904 -89.1 -546.5 0.920 -0.000 0.462 -0.002 -0.001 0.057 [0.054, 0.060]
5 metric 3276 1928 -14.6 -129.0 0.920 -0.001 0.460 -0.002 -0.008 0.057 [0.053, 0.060]
6 strong 3322 1952 -1.8 -116.1 0.919 -0.001 0.454 -0.006 -0.010 0.057 [0.054, 0.060]
7 strict 3360 1976 -10.4 -124.7 0.918 -0.001 0.450 -0.004 -0.012 0.057 [0.054, 0.060]

.Openness
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 4783 2696 0.869 0.300 0.060 [0.057, 0.063]
2 long_metric 4888 2804 -110.7 -625.4 0.869 0.000 0.301 0.000 0.059 [0.056, 0.061]
3 long_strong 5002 2912 -102.7 -617.4 0.868 -0.000 0.300 -0.001 0.058 [0.055, 0.060]
4 long_strict 5229 3032 -12.4 -584.2 0.862 -0.007 0.282 -0.018 -0.018 0.058 [0.055, 0.060]
5 metric 5274 3062 -15.0 -158.0 0.861 -0.001 0.279 -0.002 -0.021 0.058 [0.055, 0.060]
6 strong 5348 3092 14.2 -128.8 0.858 -0.003 0.272 -0.007 -0.027 0.058 [0.055, 0.061]
7 strict 5395 3122 -13.2 -156.2 0.857 -0.001 0.270 -0.003 -0.012 0.058 [0.055, 0.061]

Modification Indices

For some reason lavaan orders the groups like this:

  1. 20s
  2. 50s
  3. 30s
  4. 40s

Financial aspirations

Looking at issues with strict longitudinal invariance.

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
aspfin_W2 =~ basp14 3 3 5.40 0.14 0.11 0.1 2.80 0.39 (m)
aspfin_W3 =~ casp12 3 3 5.30 0.14 0.12 0.1 2.84 0.39 (m)
aspfin_W1 =~ aasp14 2 2 5.25 -0.20 -0.15 0.1 1.29 0.21 (m)
aspfin_W3 =~ casp14 4 4 5.02 0.18 0.12 0.1 1.60 0.24 (m)
aspfin_W1 =~ aasp12 4 4 3.65 -0.11 -0.09 0.1 3.30 0.44 (i)
aspfin_W1 =~ aasp16 3 3 3.51 0.09 0.08 0.1 4.34 0.55 (i)
aspfin_W4 =~ dasp14 1 1 3.41 0.10 0.08 0.1 3.38 0.45 (i)
aspfin_W4 =~ dasp12 1 1 3.24 0.08 0.07 0.1 4.79 0.59 (i)
aspfin_W1 =~ aasp13 4 4 2.86 0.08 0.07 0.1 4.67 0.58 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
dasp14 ~1 1 1 19.28 -0.25 -0.18 0.1 3.10 0.42 (m)
dasp14 ~1 3 3 8.27 -0.19 -0.14 0.1 2.26 0.32 (m)
aasp14 ~1 4 4 7.42 0.17 0.13 0.1 2.61 0.37 (m)
aasp14 ~1 3 3 6.42 0.15 0.11 0.1 2.91 0.40 (m)
aasp13 ~1 2 2 6.21 -0.14 -0.13 0.1 3.05 0.42 (m)
aspfin_W1 ~1 1 1 4.72 0.17 0.17 0.1 1.73 0.26 (m)
basp16 ~1 1 1 4.09 -0.10 -0.09 0.1 4.50 0.56 (m)
dasp16 ~1 3 3 3.29 0.10 0.09 0.1 3.22 0.43 (i)
casp15 ~1 4 4 3.14 -0.12 -0.10 0.1 2.26 0.32 (i)
dasp15 ~1 1 1 3.00 0.08 0.07 0.1 4.44 0.56 (i)
aasp12 ~1 4 4 2.86 -0.09 -0.07 0.1 3.68 0.48 (i)
aasp16 ~1 2 2 2.83 0.10 0.09 0.1 2.62 0.37 (i)
aasp14 ~1 1 1 2.54 0.08 0.06 0.1 3.73 0.49 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
aasp16 ~~ aasp16 4 4 13.40 0.18 0.36 0.1 4.37 0.55 (m)
casp12 ~~ casp12 2 2 3.72 0.15 0.58 0.1 1.71 0.26 (i)
casp16 ~~ casp16 4 4 3.48 -0.09 -0.41 0.1 4.30 0.55 (i)
dasp16 ~~ dasp16 3 3 3.13 0.10 0.35 0.1 3.25 0.44 (i)
aspfin_W1 ~~ aspfin_W1 1 1 2.78 0.19 1.00 0.1 0.76 0.14 (i)
basp13 ~~ basp13 4 4 2.59 0.06 0.24 0.1 6.64 0.73 (i)
casp13 ~~ casp13 3 3 2.56 -0.05 -0.21 0.1 9.38 0.86 (nm)
basp13 ~~ basp13 1 1 2.51 -0.05 -0.23 0.1 10.01 0.89 (nm)

Materialism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
bfa_mt_W1 =~ abfas117 2 2 5.77 -0.20 -0.18 0.1 1.49 0.23 (m)
bfa_mt_W2 =~ bbfas113 3 3 4.87 0.14 0.11 0.1 2.39 0.34 (m)
bfa_mt_W4 =~ dbfas113 4 4 4.16 -0.20 -0.15 0.1 1.02 0.17 (m)
bfa_mt_W1 =~ abfas116 2 2 4.10 0.17 0.15 0.1 1.39 0.22 (m)
bfa_mt_W1 =~ abfas115 2 2 2.95 0.14 0.12 0.1 1.45 0.23 (i)
bfa_mt_W4 =~ dbfas118 3 3 2.56 -0.12 -0.10 0.1 1.85 0.27 (i)
bfa_mt_W3 =~ cbfas117 1 1 2.53 0.09 0.09 0.1 2.86 0.39 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
bfa_mt_W1 ~1 1 1 12.43 -0.28 -0.28 0.1 1.59 0.24 (m)
bfa_mt_W1 ~1 2 2 10.52 0.34 0.34 0.1 0.90 0.16 (m)
abfas118 ~1 2 2 7.81 0.21 0.18 0.1 1.78 0.27 (m)
bbfas113 ~1 1 1 7.06 0.14 0.11 0.1 3.50 0.46 (m)
abfas113 ~1 1 1 6.71 0.14 0.11 0.1 3.27 0.44 (m)
dbfas113 ~1 4 4 6.41 -0.20 -0.17 0.1 1.54 0.24 (m)
dbfas114 ~1 1 1 6.38 0.12 0.11 0.1 4.34 0.55 (m)
dbfas118 ~1 4 4 6.20 -0.19 -0.18 0.1 1.74 0.26 (m)
bfa_mt_W1 ~1 4 4 6.05 0.22 0.22 0.1 1.24 0.20 (m)
cbfas113 ~1 1 1 5.19 -0.13 -0.10 0.1 3.05 0.42 (m)
cbfas113 ~1 2 2 4.66 -0.23 -0.18 0.1 0.88 0.16 (m)
bbfas114 ~1 3 3 4.48 0.11 0.10 0.1 3.92 0.51 (m)
dbfas116 ~1 1 1 4.34 0.12 0.10 0.1 2.91 0.40 (m)
cbfas114 ~1 1 1 4.12 -0.10 -0.09 0.1 4.52 0.57 (m)
bbfas113 ~1 3 3 3.78 -0.11 -0.09 0.1 2.93 0.40 (i)
abfas115 ~1 3 3 3.53 0.11 0.09 0.1 2.92 0.40 (i)
cbfas116 ~1 1 1 3.47 -0.11 -0.09 0.1 3.00 0.41 (i)
abfas118 ~1 4 4 2.53 0.10 0.08 0.1 2.75 0.38 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
cbfas118 ~~ cbfas118 2 2 6.19 0.26 0.42 0.1 0.92 0.16 (m)
dbfas118 ~~ dbfas118 3 3 6.10 0.19 0.49 0.1 1.65 0.25 (m)
bbfas116 ~~ bbfas116 2 2 3.31 0.20 0.59 0.1 0.81 0.15 (i)
cbfas117 ~~ cbfas117 4 4 3.06 0.14 0.68 0.1 1.56 0.24 (i)
cbfas118 ~~ cbfas118 3 3 3.02 -0.13 -0.47 0.1 1.79 0.27 (i)
dbfas115 ~~ dbfas115 1 1 2.99 -0.13 -0.53 0.1 1.82 0.27 (i)
dbfas114 ~~ dbfas114 3 3 2.50 0.08 0.63 0.1 3.83 0.50 (i)

Horizontal Collectivism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_col_W1 =~ aind9 1 1 7.32 0.13 0.13 0.1 4.50 0.56 (m)
hrz_col_W2 =~ bind11 2 2 4.93 0.25 0.21 0.1 0.78 0.14 (m)
hrz_col_W2 =~ bind10 1 1 4.71 -0.10 -0.11 0.1 4.86 0.60 (m)
hrz_col_W1 =~ aind12 3 3 4.42 -0.09 -0.11 0.1 5.42 0.64 (m)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_col_W1 ~1 1 1 25.80 -0.42 -0.42 0.1 1.48 0.23 (m)
hrz_col_W1 ~1 2 2 21.08 0.50 0.50 0.1 0.83 0.15 (m)
aind9 ~1 1 1 21.06 -0.20 -0.20 0.1 5.51 0.65 (m)
aind11 ~1 1 1 7.87 0.14 0.13 0.1 4.03 0.52 (m)
cind9 ~1 2 2 7.81 0.15 0.17 0.1 3.30 0.44 (m)
dind11 ~1 1 1 7.23 -0.15 -0.14 0.1 3.02 0.41 (m)
bind9 ~1 1 1 6.79 -0.11 -0.12 0.1 5.19 0.62 (m)
bind12 ~1 3 3 5.07 -0.10 -0.13 0.1 4.77 0.59 (m)
aind12 ~1 2 2 4.78 0.11 0.14 0.1 3.63 0.48 (m)
aind12 ~1 4 4 4.66 0.09 0.11 0.1 5.63 0.66 (m)
aind10 ~1 2 2 4.24 0.11 0.13 0.1 3.39 0.45 (m)
dind12 ~1 4 4 3.41 -0.10 -0.13 0.1 3.44 0.46 (i)
aind12 ~1 3 3 3.03 0.07 0.08 0.1 6.64 0.73 (i)
bind10 ~1 1 1 2.83 0.07 0.08 0.1 5.78 0.67 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
aind9 ~~ aind9 1 1 10.03 0.14 0.55 0.1 5.13 0.62 (m)
hrz_col_W1 ~~ hrz_col_W1 4 4 7.75 -0.42 -1.00 0.1 0.44 0.10 (m)
hrz_col_W1 ~~ hrz_col_W1 1 1 6.68 0.35 1.00 0.1 0.56 0.12 (m)
dind11 ~~ dind11 1 1 3.28 0.12 0.78 0.1 2.12 0.31 (i)
aind12 ~~ aind12 4 4 2.81 -0.06 -0.60 0.1 8.24 0.82 (nm)
aind10 ~~ aind10 2 2 2.77 -0.08 -0.43 0.1 4.61 0.57 (i)
aind10 ~~ aind10 3 3 2.67 0.06 0.43 0.1 6.51 0.72 (i)
bind12 ~~ bind12 1 1 2.61 0.06 0.61 0.1 6.93 0.75 (i)

Horizontal Individualism

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_ind_W2 =~ bind3 3 3 5.81 0.19 0.17 0.1 1.68 0.25 (m)
hrz_ind_W2 =~ bind1 3 3 3.16 -0.10 -0.12 0.1 3.21 0.43 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
aind4 ~1 1 1 5.94 0.10 0.12 0.1 5.51 0.65 (m)
bind1 ~1 1 1 4.46 -0.09 -0.10 0.1 6.05 0.69 (m)
dind4 ~1 1 1 4.40 -0.10 -0.12 0.1 4.52 0.57 (m)
cind1 ~1 2 2 3.77 -0.15 -0.19 0.1 1.79 0.27 (i)
dind1 ~1 2 2 3.26 0.13 0.16 0.1 1.95 0.29 (i)
dind3 ~1 4 4 3.08 -0.12 -0.11 0.1 2.15 0.31 (i)
aind2 ~1 1 1 3.08 -0.08 -0.08 0.1 4.51 0.57 (i)
aind3 ~1 1 1 2.82 0.09 0.08 0.1 3.77 0.49 (i)
dind3 ~1 3 3 2.81 -0.11 -0.10 0.1 2.18 0.32 (i)
cind4 ~1 4 4 2.78 -0.11 -0.13 0.1 2.28 0.33 (i)
cind2 ~1 2 2 2.68 0.14 0.14 0.1 1.43 0.22 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
cind1 ~~ cind1 2 2 6.52 0.18 0.69 0.1 1.97 0.29 (m)
cind1 ~~ cind1 3 3 3.81 0.10 0.63 0.1 4.00 0.52 (i)
dind4 ~~ dind4 2 2 2.88 0.13 0.91 0.1 1.62 0.25 (i)

Mature Values Index

It’s not clear that we can trust the invariance tests for this scale.

Unmitigated Self-Interest

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W3 =~ cusi7 1 1 4.21 -0.14 -0.11 0.1 2.30 0.33 (m)
usi_W2 =~ busi1 4 4 3.83 0.14 0.13 0.1 1.93 0.28 (i)
usi_W4 =~ dusi6 3 3 3.41 0.15 0.14 0.1 1.55 0.24 (i)
usi_W2 =~ busi5 4 4 3.13 -0.10 -0.10 0.1 3.37 0.45 (i)
usi_W2 =~ busi3 3 3 2.90 0.12 0.13 0.1 1.96 0.29 (i)
usi_W2 =~ busi2 1 1 2.87 -0.08 -0.10 0.1 4.30 0.55 (i)
usi_W1 =~ ausi2 3 3 2.54 -0.09 -0.10 0.1 3.51 0.47 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W1 ~1 1 1 21.17 0.39 0.39 0.1 1.36 0.21 (m)
ausi1 ~1 1 1 11.59 0.17 0.14 0.1 4.20 0.54 (m)
ausi2 ~1 2 2 8.96 0.18 0.21 0.1 2.82 0.39 (m)
dusi1 ~1 1 1 8.55 -0.17 -0.14 0.1 3.14 0.43 (m)
usi_W1 ~1 2 2 7.31 -0.26 -0.26 0.1 1.06 0.18 (m)
ausi1 ~1 3 3 6.55 0.15 0.13 0.1 3.02 0.41 (m)
usi_W1 ~1 4 4 6.00 -0.22 -0.22 0.1 1.21 0.20 (m)
ausi7 ~1 4 4 3.84 -0.14 -0.11 0.1 2.07 0.30 (m)
ausi3 ~1 4 4 3.64 -0.11 -0.12 0.1 2.90 0.40 (i)
dusi1 ~1 2 2 3.45 -0.17 -0.14 0.1 1.14 0.19 (i)
dusi6 ~1 2 2 2.88 -0.17 -0.16 0.1 0.94 0.16 (i)
ausi1 ~1 2 2 2.66 0.12 0.11 0.1 1.78 0.27 (i)
cusi1 ~1 3 3 2.61 -0.11 -0.10 0.1 2.16 0.31 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W1 ~~ usi_W1 2 2 6.02 -0.25 -1.00 0.1 0.97 0.17 (m)
usi_W3 ~~ usi_W3 2 2 4.34 0.11 1.00 0.1 3.59 0.47 (m)
ausi7 ~~ ausi7 2 2 3.72 0.25 0.70 0.1 0.57 0.12 (i)
ausi5 ~~ ausi5 2 2 3.72 -0.11 -0.70 0.1 3.05 0.42 (i)
ausi1 ~~ ausi1 3 3 3.49 0.13 0.67 0.1 1.98 0.29 (i)
busi6 ~~ busi6 2 2 3.36 -0.20 -0.71 0.1 0.83 0.15 (i)
busi6 ~~ busi6 3 3 3.18 0.14 0.71 0.1 1.63 0.25 (i)
busi2 ~~ busi2 1 1 3.16 0.08 0.80 0.1 5.38 0.64 (i)
cusi5 ~~ cusi5 1 1 3.09 0.09 0.68 0.1 4.07 0.52 (i)
busi6 ~~ busi6 4 4 2.53 -0.14 -0.66 0.1 1.22 0.20 (i)

Vertical Collectivism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_col_W3 =~ cind14 1 1 6.67 0.11 0.14 0.1 5.30 0.63 (m)
vrt_col_W3 =~ cind14 4 4 5.34 -0.14 -0.16 0.1 2.87 0.39 (m)
vrt_col_W1 =~ aind14 4 4 5.16 -0.10 -0.12 0.1 5.10 0.62 (m)
vrt_col_W1 =~ aind15 2 2 2.66 0.12 0.11 0.1 1.75 0.26 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
cind14 ~1 1 1 8.53 -0.14 -0.15 0.1 4.26 0.54 (m)
aind13 ~1 1 1 6.90 -0.12 -0.11 0.1 4.65 0.58 (m)
aind15 ~1 1 1 5.04 0.11 0.10 0.1 4.47 0.56 (m)
aind16 ~1 2 2 4.66 0.15 0.16 0.1 2.00 0.29 (m)
cind13 ~1 1 1 4.33 0.11 0.09 0.1 3.68 0.48 (m)
vrt_col_W1 ~1 1 1 4.27 -0.17 -0.17 0.1 1.46 0.23 (m)
cind15 ~1 4 4 4.00 -0.12 -0.11 0.1 2.70 0.38 (m)
cind13 ~1 2 2 3.84 -0.16 -0.14 0.1 1.56 0.24 (i)
cind16 ~1 2 2 3.59 0.15 0.15 0.1 1.64 0.25 (i)
bind16 ~1 1 1 3.45 -0.10 -0.10 0.1 3.78 0.49 (i)
bind13 ~1 1 1 3.23 0.09 0.08 0.1 3.94 0.51 (i)
aind16 ~1 1 1 2.68 -0.08 -0.08 0.1 4.58 0.57 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
cind14 ~~ cind14 1 1 14.63 0.19 0.58 0.1 4.25 0.54 (m)
aind13 ~~ aind13 1 1 2.79 0.09 0.54 0.1 3.62 0.48 (i)
aind15 ~~ aind15 3 3 2.70 0.10 0.43 0.1 2.97 0.41 (i)
dind15 ~~ dind15 1 1 2.64 -0.09 -0.36 0.1 3.09 0.42 (i)

Vertical Individualism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W1 =~ aind8 1 1 3.29 0.11 0.09 0.1 2.94 0.40 (i)
vrt_ind_W4 =~ dind7 4 4 2.96 0.17 0.12 0.1 1.01 0.17 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W1 ~1 1 1 9.83 0.27 0.27 0.1 1.39 0.22 (m)
vrt_ind_W1 ~1 2 2 9.27 -0.34 -0.34 0.1 0.78 0.14 (m)
aind8 ~1 1 1 8.56 0.15 0.13 0.1 3.96 0.51 (m)
bind8 ~1 4 4 4.51 -0.15 -0.13 0.1 2.12 0.31 (m)
aind6 ~1 2 2 4.42 -0.13 -0.11 0.1 2.82 0.39 (m)
aind8 ~1 3 3 3.03 -0.10 -0.09 0.1 2.78 0.38 (i)
cind5 ~1 2 2 2.75 -0.14 -0.15 0.1 1.42 0.22 (i)
bind5 ~1 1 1 2.57 0.07 0.08 0.1 5.18 0.62 (i)
bind7 ~1 4 4 2.55 0.11 0.10 0.1 1.99 0.29 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W1 ~~ vrt_ind_W1 1 1 6.79 0.37 1.00 0.1 0.49 0.11 (m)
vrt_ind_W1 ~~ vrt_ind_W1 4 4 4.75 -0.35 -1.00 0.1 0.38 0.09 (m)
aind5 ~~ aind5 3 3 3.53 0.10 0.75 0.1 3.80 0.50 (i)

Loadings

All from the most constrained model (longitudinal and group constraints).

Financial Aspirations
item aspfin_W1 aspfin_W2 aspfin_W3 aspfin_W4 aspfin_W1_std aspfin_W2_std aspfin_W3_std aspfin_W4_std
aasp12 0.77 0.65
aasp13 0.98 0.88
aasp14 0.66 0.49
aasp15 0.78 0.64
aasp16 0.89 0.80
basp12 0.77 0.64
basp13 0.98 0.87
basp14 0.66 0.48
basp15 0.78 0.63
basp16 0.89 0.79
casp12 0.77 0.61
casp13 0.98 0.86
casp14 0.66 0.45
casp15 0.78 0.60
casp16 0.89 0.77
dasp12 0.77 0.62
dasp13 0.98 0.86
dasp14 0.66 0.46
dasp15 0.78 0.61
dasp16 0.89 0.77
Materialism
item bfa_mt_W1 bfa_mt_W2 bfa_mt_W3 bfa_mt_W4 bfa_mt_W1_std bfa_mt_W2_std bfa_mt_W3_std bfa_mt_W4_std
abfas113 -0.62 -0.50
abfas114 -0.66 -0.63
abfas115 -0.79 -0.65
abfas116 0.71 0.62
abfas117 0.61 0.57
abfas118 0.83 0.73
bbfas113 -0.62 -0.47
bbfas114 -0.66 -0.59
bbfas115 -0.79 -0.61
bbfas116 0.71 0.58
bbfas117 0.61 0.54
bbfas118 0.83 0.70
cbfas113 -0.62 -0.49
cbfas114 -0.66 -0.62
cbfas115 -0.79 -0.64
cbfas116 0.71 0.61
cbfas117 0.61 0.56
cbfas118 0.83 0.73
dbfas113 -0.62 -0.46
dbfas114 -0.66 -0.58
dbfas115 -0.79 -0.61
dbfas116 0.71 0.57
dbfas117 0.61 0.53
dbfas118 0.83 0.69
Horizontal Collectivism
item hrz_col_W1 hrz_col_W2 hrz_col_W3 hrz_col_W4 hrz_col_W1_std hrz_col_W2_std hrz_col_W3_std hrz_col_W4_std
aind9 0.66 0.67
aind10 0.66 0.75
aind11 0.49 0.45
aind12 0.51 0.63
bind9 0.66 0.61
bind10 0.66 0.70
bind11 0.49 0.40
bind12 0.51 0.57
cind9 0.66 0.61
cind10 0.66 0.70
cind11 0.49 0.40
cind12 0.51 0.57
dind9 0.66 0.61
dind10 0.66 0.70
dind11 0.49 0.40
dind12 0.51 0.57
Horizontal Individualism
item hrz_ind_W1 hrz_ind_W2 hrz_ind_W3 hrz_ind_W4 hrz_ind_W1_std hrz_ind_W2_std hrz_ind_W3_std hrz_ind_W4_std
aind1 0.51 0.63
aind2 0.71 0.67
aind3 0.39 0.36
aind4 0.27 0.32
bind1 0.51 0.58
bind2 0.71 0.63
bind3 0.39 0.32
bind4 0.27 0.28
cind1 0.51 0.61
cind2 0.71 0.65
cind3 0.39 0.34
cind4 0.27 0.30
dind1 0.51 0.58
dind2 0.71 0.63
dind3 0.39 0.32
dind4 0.27 0.28
Mature Values Index
item mvi_W1 mvi_W2 mvi_W3 mvi_W4 mvi_W1_std mvi_W2_std mvi_W3_std mvi_W4_std
aval7 0.90 0.53
aval9 0.77 0.58
aval11 0.87 0.53
aval13 0.59 0.44
aval15 0.84 0.53
aval17 0.84 0.53
aval18 0.97 0.51
aval20 0.86 0.59
aval21 0.71 0.53
aval23 0.74 0.48
aval8 0.74 0.38
aval10 0.59 0.30
aval12 0.42 0.21
aval14 0.87 0.48
aval16 0.82 0.48
aval19 0.82 0.44
aval22 0.83 0.43
bval7 0.90 0.52
bval9 0.77 0.57
bval11 0.87 0.52
bval13 0.59 0.42
bval15 0.84 0.51
bval17 0.84 0.52
bval18 0.97 0.50
bval20 0.86 0.57
bval21 0.71 0.51
bval23 0.74 0.46
bval8 0.74 0.37
bval10 0.59 0.29
bval12 0.42 0.20
bval14 0.87 0.47
bval16 0.82 0.47
bval19 0.82 0.43
bval22 0.83 0.41
cval7 0.90 0.53
cval9 0.77 0.59
cval11 0.87 0.54
cval13 0.59 0.44
cval15 0.84 0.53
cval17 0.84 0.54
cval18 0.97 0.52
cval20 0.86 0.59
cval21 0.71 0.53
cval23 0.74 0.48
cval8 0.74 0.38
cval10 0.59 0.31
cval12 0.42 0.21
cval14 0.87 0.49
cval16 0.82 0.49
cval19 0.82 0.44
cval22 0.83 0.43
dval7 0.90 0.55
dval9 0.77 0.60
dval11 0.87 0.55
dval13 0.59 0.46
dval15 0.84 0.55
dval17 0.84 0.55
dval18 0.97 0.53
dval20 0.86 0.61
dval21 0.71 0.55
dval23 0.74 0.50
dval8 0.74 0.40
dval10 0.59 0.32
dval12 0.42 0.22
dval14 0.87 0.50
dval16 0.82 0.50
dval19 0.82 0.46
dval22 0.83 0.45
Unmitigated Self-Interest
item usi_W1 usi_W2 usi_W3 usi_W4 usi_W1_std usi_W2_std usi_W3_std usi_W4_std
ausi1 0.67 0.58
ausi2 -0.36 -0.43
ausi3 -0.37 -0.39
ausi5 0.56 0.55
ausi6 -0.57 -0.56
ausi7 0.69 0.55
busi1 0.67 0.60
busi2 -0.36 -0.45
busi3 -0.37 -0.42
busi5 0.56 0.57
busi6 -0.57 -0.58
busi7 0.69 0.58
cusi1 0.67 0.58
cusi2 -0.36 -0.43
cusi3 -0.37 -0.40
cusi5 0.56 0.55
cusi6 -0.57 -0.56
cusi7 0.69 0.55
dusi1 0.67 0.56
dusi2 -0.36 -0.41
dusi3 -0.37 -0.38
dusi5 0.56 0.53
dusi6 -0.57 -0.54
dusi7 0.69 0.54
Vertical Collectivism
item vrt_col_W1 vrt_col_W2 vrt_col_W3 vrt_col_W4 vrt_col_W1_std vrt_col_W2_std vrt_col_W3_std vrt_col_W4_std
aind13 0.74 0.68
aind14 0.51 0.58
aind15 0.82 0.75
aind16 0.33 0.34
bind13 0.74 0.69
bind14 0.51 0.59
bind15 0.82 0.76
bind16 0.33 0.35
cind13 0.74 0.69
cind14 0.51 0.59
cind15 0.82 0.76
cind16 0.33 0.35
dind13 0.74 0.71
dind14 0.51 0.61
dind15 0.82 0.78
dind16 0.33 0.36
Vertical Individualism
item vrt_ind_W1 vrt_ind_W2 vrt_ind_W3 vrt_ind_W4 vrt_ind_W1_std vrt_ind_W2_std vrt_ind_W3_std vrt_ind_W4_std
aind5 0.46 0.50
aind6 0.85 0.75
aind7 0.67 0.56
aind8 0.56 0.48
bind5 0.46 0.46
bind6 0.85 0.72
bind7 0.67 0.53
bind8 0.56 0.44
cind5 0.46 0.48
cind6 0.85 0.73
cind7 0.67 0.55
cind8 0.56 0.46
dind5 0.46 0.41
dind6 0.85 0.67
dind7 0.67 0.47
dind8 0.56 0.39

LOESS Plots

Invariance dropping items

Results

MFI etc

Financial Aspirations
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 140 120 0.996 0.989 0.028 [0.000, 0.045]
2 long_metric 175 144 -12.7 -127.1 0.994 -0.002 0.982 -0.006 0.032 [0.007, 0.047]
3 long_strong 195 168 -28.4 -142.7 0.995 0.001 0.985 0.002 0.027 [0.000, 0.042]
4 long_strict 227 204 -39.8 -211.3 0.996 0.001 0.987 0.002 -0.002 0.023 [0.000, 0.038]
5 metric 236 213 -8.5 -51.4 0.996 -0.000 0.987 -0.000 0.004 0.023 [0.000, 0.038]
6 strong 251 222 -3.4 -46.2 0.994 -0.001 0.983 -0.003 -0.001 0.025 [0.000, 0.039]
7 strict 263 231 -6.5 -49.4 0.994 -0.000 0.982 -0.001 -0.005 0.025 [0.000, 0.039]

Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .016 (versus .023 previously). Dropped asp14: You will be your own boss.; asp16: You will have a job that pays well.

Materialism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 970 536 0.933 0.779 0.061 [0.055, 0.067]
2 long_metric 1033 584 -32.4 -261.2 0.931 -0.002 0.772 -0.007 0.060 [0.054, 0.065]
3 long_strong 1089 632 -40.7 -269.4 0.930 -0.001 0.768 -0.003 0.058 [0.052, 0.063]
4 long_strict 1171 692 -37.6 -323.5 0.926 -0.003 0.759 -0.010 -0.020 0.057 [0.051, 0.062]
5 metric 1183 707 -18.5 -90.0 0.927 0.001 0.760 0.002 -0.012 0.056 [0.050, 0.061]
6 strong 1216 722 3.7 -67.8 0.924 -0.003 0.752 -0.008 -0.016 0.056 [0.051, 0.062]
7 strict 1253 737 6.3 -65.2 0.921 -0.003 0.743 -0.009 -0.016 0.057 [0.051, 0.062]

Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .016 (versus >.024 previously). Also solved convergence problems. Dropped bfas113: I would be happier if I could afford to buy more things.

Horizontal Collectivism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 140 120 0.994 0.989 0.028 [0.000, 0.045]
2 long_metric 178 144 -9.6 -124.0 0.990 -0.004 0.980 -0.008 0.033 [0.012, 0.048]
3 long_strong 232 168 5.6 -108.7 0.982 -0.008 0.964 -0.017 0.042 [0.028, 0.054]
4 long_strict 278 204 -26.2 -197.7 0.979 -0.003 0.958 -0.005 -0.030 0.041 [0.028, 0.052]
5 metric 300 213 4.7 -38.2 0.975 -0.004 0.951 -0.008 -0.030 0.044 [0.031, 0.055]
6 strong 368 222 49.1 6.2 0.959 -0.016 0.919 -0.031 -0.044 0.055 [0.045, 0.065]
7 strict 405 231 19.6 -23.2 0.951 -0.008 0.904 -0.015 -0.054 0.059 [0.049, 0.068]

Some improvement. Better overall fit, improved invariance, but still has \(\Delta\text{MFI}\) = .032 (versus .056 previously). Dropped ind11: To me, pleasure is spending time with others.

Horizontal Individualism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 172 120 0.976 0.970 0.045 [0.029, 0.059]
2 long_metric 212 144 -8.1 -122.4 0.969 -0.007 0.961 -0.009 0.047 [0.033, 0.060]
3 long_strong 233 168 -26.9 -141.3 0.970 0.001 0.963 0.002 0.042 [0.028, 0.055]
4 long_strict 272 204 -33.4 -204.9 0.969 -0.001 0.961 -0.001 -0.009 0.039 [0.026, 0.051]
5 metric 287 213 -2.9 -45.8 0.966 -0.003 0.958 -0.003 -0.003 0.040 [0.027, 0.052]
6 strong 311 222 6.1 -36.7 0.959 -0.007 0.950 -0.008 -0.013 0.043 [0.031, 0.054]
7 strict 323 231 -6.5 -49.4 0.958 -0.001 0.948 -0.001 -0.013 0.043 [0.031, 0.054]

About the same. Better overall fit. May not be necessary to drop items (but \(\Delta\text{MFI}\) is .12 from long strict to strict in both cases). Dropped ind1: I’d rather depend on myself than others.

Unmitigated Self-Interest
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 210 120 0.958 0.949 0.059 [0.045, 0.072]
2 long_metric 191 144 -67.1 -181.4 0.978 0.020 0.973 0.024 0.039 [0.022, 0.053]
3 long_strong 212 168 -27.4 -141.7 0.980 0.002 0.975 0.002 0.035 [0.017, 0.048]
4 long_strict 284 204 0.7 -170.8 0.963 -0.017 0.955 -0.020 0.005 0.043 [0.030, 0.054]
5 metric 270 213 -32.9 -75.8 0.974 0.011 0.968 0.013 -0.005 0.035 [0.020, 0.047]
6 strong 322 222 34.7 -8.2 0.953 -0.020 0.944 -0.024 -0.031 0.046 [0.034, 0.056]
7 strict 331 231 -9.7 -52.6 0.954 0.000 0.944 0.000 -0.010 0.045 [0.033, 0.055]

Worse invariance, but better overall fit indices. Dropped usi1: The pleasures of the senses are the highest good.; usi2: People ought to be motivated by something beyond their own self-interest.; usi5: Worldly possessions are the greatest good and the highest value in life.

Vertical Collectivism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 162 120 0.989 0.976 0.040 [0.022, 0.055]
2 long_metric 180 144 -29.8 -144.2 0.991 0.001 0.979 0.003 0.034 [0.014, 0.049]
3 long_strong 208 168 -20.1 -134.5 0.990 -0.001 0.977 -0.002 0.033 [0.014, 0.047]
4 long_strict 254 204 -25.5 -197.0 0.987 -0.003 0.971 -0.006 -0.005 0.034 [0.018, 0.046]
5 metric 286 213 14.1 -28.8 0.981 -0.006 0.958 -0.013 -0.021 0.040 [0.027, 0.051]
6 strong 320 222 15.5 -27.4 0.975 -0.006 0.945 -0.013 -0.032 0.045 [0.034, 0.056]
7 strict 335 231 -2.8 -45.6 0.973 -0.002 0.942 -0.003 -0.030 0.046 [0.034, 0.056]

Some improvement. Still not perfect. Only three items. Very good fit indices. Dropped ind16: It is important to me that I respect the decisions made by my groups.

Vertical Individualism
Type \(\chi^2\) \(\text{Df}\) \(\Delta\text{AIC}\) \(\Delta\text{BIC}\) \(\text{CFI}\) \(\Delta\text{CFI}\) \(\text{MFI}\) \(\Delta\text{MFI}\) \(\Delta_{1,4}\text{MFI}\) \(\text{RMSEA}\)
1 unconstrained 135 120 0.996 0.991 0.024 [0.000, 0.043]
2 long_metric 168 144 -15.0 -129.4 0.993 -0.003 0.986 -0.005 0.028 [0.000, 0.044]
3 long_strong 192 168 -23.4 -137.7 0.993 -0.000 0.986 -0.000 0.026 [0.000, 0.042]
4 long_strict 230 204 -33.9 -205.4 0.992 -0.001 0.985 -0.001 -0.007 0.024 [0.000, 0.039]
5 metric 242 213 -6.8 -49.7 0.991 -0.001 0.984 -0.001 -0.003 0.025 [0.000, 0.039]
6 strong 263 222 3.7 -39.1 0.988 -0.004 0.976 -0.007 -0.010 0.029 [0.010, 0.042]
7 strict 274 231 -7.6 -50.5 0.987 -0.000 0.976 -0.001 -0.009 0.029 [0.010, 0.042]

Better. Difference between strict and long_strict is ~< .01. Dropped ind8: When another person does better than I do, I get tense and aroused.

Modification Indices

For some reason lavaan orders the groups like this:

  1. 20s
  2. 50s
  3. 30s
  4. 40s

Financial aspirations

Looking at issues with strict longitudinal invariance.

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
aspfin_W1 =~ aasp12 4 4 4.23 -0.12 -0.10 0.1 3.09 0.42 (m)
aspfin_W3 =~ casp12 3 3 4.08 0.12 0.10 0.1 2.87 0.39 (m)
aspfin_W4 =~ dasp15 1 1 2.80 -0.08 -0.07 0.1 4.27 0.54 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
aspfin_W1 ~1 1 1 7.24 0.21 0.21 0.1 1.58 0.24 (m)
aspfin_W1 ~1 4 4 3.50 -0.17 -0.17 0.1 1.23 0.20 (i)
aspfin_W1 ~1 2 2 3.01 -0.19 -0.19 0.1 0.88 0.16 (i)
casp15 ~1 4 4 2.82 -0.11 -0.10 0.1 2.18 0.31 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
casp12 ~~ casp12 2 2 4.86 0.16 0.51 0.1 1.92 0.28 (m)
aspfin_W1 ~~ aspfin_W1 1 1 2.76 0.21 1.00 0.1 0.64 0.13 (i)

Materialism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
bfa_mt_W1 =~ abfas117 2 2 6.01 -0.20 -0.19 0.1 1.50 0.23 (m)
bfa_mt_W1 =~ abfas116 2 2 4.15 0.17 0.15 0.1 1.45 0.23 (m)
bfa_mt_W1 =~ abfas115 2 2 3.03 0.14 0.12 0.1 1.44 0.22 (i)
bfa_mt_W2 =~ bbfas115 1 1 2.90 0.10 0.09 0.1 2.80 0.39 (i)
bfa_mt_W4 =~ dbfas115 3 3 2.81 -0.12 -0.10 0.1 1.85 0.27 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
bfa_mt_W1 ~1 1 1 10.49 -0.26 -0.26 0.1 1.57 0.24 (m)
bfa_mt_W1 ~1 2 2 9.26 0.32 0.32 0.1 0.89 0.16 (m)
abfas118 ~1 2 2 9.25 0.22 0.20 0.1 1.83 0.27 (m)
cbfas114 ~1 1 1 6.52 -0.12 -0.11 0.1 4.41 0.56 (m)
dbfas114 ~1 1 1 5.84 0.12 0.11 0.1 4.31 0.55 (m)
bfa_mt_W1 ~1 4 4 5.59 0.21 0.21 0.1 1.22 0.20 (m)
dbfas118 ~1 4 4 4.14 -0.15 -0.14 0.1 1.77 0.26 (m)
dbfas116 ~1 1 1 4.14 0.12 0.10 0.1 2.91 0.40 (m)
abfas115 ~1 3 3 3.81 0.11 0.09 0.1 2.90 0.40 (i)
bbfas114 ~1 3 3 3.03 0.09 0.08 0.1 3.94 0.51 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
cbfas118 ~~ cbfas118 2 2 6.89 0.27 0.39 0.1 0.96 0.16 (m)
dbfas118 ~~ dbfas118 3 3 6.56 0.19 0.46 0.1 1.74 0.26 (m)
bbfas116 ~~ bbfas116 2 2 4.73 0.24 0.58 0.1 0.83 0.15 (m)
cbfas118 ~~ cbfas118 3 3 3.36 -0.14 -0.44 0.1 1.76 0.26 (i)
cbfas117 ~~ cbfas117 4 4 3.27 0.15 0.68 0.1 1.54 0.24 (i)
bbfas116 ~~ bbfas116 3 3 3.02 -0.12 -0.60 0.1 2.09 0.30 (i)
dbfas115 ~~ dbfas115 1 1 2.70 -0.12 -0.56 0.1 1.74 0.26 (i)

Horizontal Collectivism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_col_W1 =~ aind9 1 1 5.74 0.11 0.11 0.1 4.49 0.56 (m)
hrz_col_W2 =~ bind10 1 1 3.92 -0.09 -0.10 0.1 4.73 0.59 (m)
hrz_col_W1 =~ aind12 3 3 3.27 -0.08 -0.10 0.1 5.35 0.64 (i)
hrz_col_W4 =~ dind9 1 1 2.84 -0.09 -0.09 0.1 3.71 0.49 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_col_W1 ~1 1 1 29.98 -0.45 -0.45 0.1 1.47 0.23 (m)
hrz_col_W1 ~1 2 2 20.94 0.50 0.50 0.1 0.83 0.15 (m)
aind9 ~1 1 1 17.37 -0.18 -0.18 0.1 5.50 0.65 (m)
aind12 ~1 2 2 6.79 0.14 0.17 0.1 3.55 0.47 (m)
bind9 ~1 1 1 5.89 -0.11 -0.11 0.1 5.15 0.62 (m)
cind9 ~1 2 2 5.82 0.13 0.15 0.1 3.42 0.46 (m)
aind10 ~1 2 2 5.48 0.13 0.15 0.1 3.17 0.43 (m)
aind12 ~1 4 4 4.98 0.09 0.12 0.1 5.57 0.66 (m)
bind10 ~1 1 1 4.35 0.09 0.10 0.1 5.87 0.68 (m)
bind12 ~1 3 3 4.07 -0.09 -0.11 0.1 4.69 0.58 (m)
dind12 ~1 4 4 3.61 -0.10 -0.13 0.1 3.39 0.45 (i)
aind12 ~1 3 3 3.60 0.07 0.09 0.1 6.57 0.73 (i)
cind10 ~1 2 2 3.13 -0.11 -0.15 0.1 2.54 0.36 (i)
hrz_col_W1 ~1 4 4 2.57 0.15 0.15 0.1 1.14 0.19 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
aind9 ~~ aind9 1 1 9.96 0.14 0.53 0.1 5.11 0.62 (m)
hrz_col_W1 ~~ hrz_col_W1 4 4 9.60 -0.47 -1.00 0.1 0.43 0.10 (m)
hrz_col_W1 ~~ hrz_col_W1 1 1 6.87 0.35 1.00 0.1 0.55 0.11 (m)
aind10 ~~ aind10 2 2 5.02 -0.11 -0.41 0.1 4.03 0.52 (m)
bind12 ~~ bind12 1 1 2.85 0.07 0.65 0.1 6.59 0.73 (i)
aind12 ~~ aind12 4 4 2.67 -0.06 -0.64 0.1 8.10 0.81 (nm)

Horizontal Individualism

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_ind_W2 =~ bind2 1 1 2.71 0.14 0.12 0.1 1.45 0.23 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
hrz_ind_W1 ~1 1 1 6.94 0.27 0.27 0.1 0.98 0.17 (m)
hrz_ind_W1 ~1 4 4 4.34 -0.24 -0.24 0.1 0.76 0.14 (m)
cind4 ~1 3 3 3.58 -0.10 -0.12 0.1 3.39 0.45 (i)
aind4 ~1 1 1 3.38 0.08 0.09 0.1 5.67 0.66 (i)
dind4 ~1 1 1 2.56 -0.07 -0.09 0.1 4.59 0.57 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W1 hrz_ind_W3 [in block 2]

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: hrz_ind_W3 hrz_ind_W4 [in block 2]
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
bind4 ~~ bind4 2 2 2.55 0.1 0.71 0.1 2.34 0.33 (i)

Mature Values Index

It’s not clear that we can trust the invariance tests for this scale.

Unmitigated Self-Interest

## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 4]
group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W1 =~ ausi3 4 4 5.7 0.17 0.18 0.1 1.93 0.28 (m)
usi_W4 =~ dusi3 3 3 3.0 0.15 0.13 0.1 1.32 0.21 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 4]
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W1 ~1 1 1 18.80 -0.43 -0.43 0.1 1.01 0.17 (m)
usi_W1 ~1 2 2 7.77 0.40 0.40 0.1 0.49 0.11 (m)
ausi7 ~1 4 4 5.07 -0.16 -0.13 0.1 1.92 0.28 (m)
ausi7 ~1 1 1 4.19 0.12 0.09 0.1 2.97 0.41 (m)
ausi3 ~1 1 1 3.76 -0.09 -0.10 0.1 4.36 0.55 (i)
dusi7 ~1 2 2 3.67 -0.20 -0.15 0.1 0.93 0.16 (i)
cusi7 ~1 3 3 2.86 0.12 0.10 0.1 1.99 0.29 (i)
ausi3 ~1 4 4 2.64 -0.10 -0.10 0.1 2.74 0.38 (i)
busi7 ~1 4 4 2.62 -0.13 -0.11 0.1 1.50 0.23 (i) 
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 1]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 2]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 3]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W2 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W1 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W2 usi_W3 [in block 4]
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply a correlation larger than 1;
##                   variables involved are: usi_W3 usi_W4 [in block 4]
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
usi_W3 ~~ usi_W3 4 4 4.81 -0.29 -1.00 0.1 0.58 0.12 (m)
usi_W1 ~~ usi_W1 2 2 3.95 0.90 1.00 0.1 0.05 0.06 (m)
usi_W1 ~~ usi_W1 4 4 3.84 -0.34 -1.00 0.1 0.33 0.09 (i)
ausi7 ~~ ausi7 2 2 3.26 0.25 0.82 0.1 0.51 0.11 (i)
busi6 ~~ busi6 4 4 3.15 -0.17 -0.57 0.1 1.03 0.17 (i)

Vertical Collectivism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_col_W3 =~ cind14 1 1 6.68 0.11 0.14 0.1 5.37 0.64 (m)
vrt_col_W3 =~ cind14 4 4 6.00 -0.15 -0.17 0.1 2.82 0.39 (m)
vrt_col_W1 =~ aind14 4 4 4.63 -0.10 -0.11 0.1 4.91 0.60 (m)
vrt_col_W1 =~ aind15 2 2 3.12 0.13 0.12 0.1 1.77 0.26 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
cind14 ~1 1 1 9.14 -0.15 -0.16 0.1 4.24 0.54 (m)
aind13 ~1 1 1 7.84 -0.13 -0.12 0.1 4.66 0.58 (m)
aind15 ~1 1 1 4.11 0.10 0.09 0.1 4.44 0.56 (m)
cind13 ~1 1 1 4.09 0.11 0.09 0.1 3.67 0.48 (m)
cind15 ~1 4 4 3.86 -0.12 -0.11 0.1 2.70 0.38 (m)
cind13 ~1 2 2 2.88 -0.14 -0.12 0.1 1.58 0.24 (i)
vrt_col_W1 ~1 1 1 2.79 -0.14 -0.14 0.1 1.45 0.23 (i)
cind14 ~1 2 2 2.65 0.08 0.09 0.1 4.23 0.54 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
cind14 ~~ cind14 1 1 13.79 0.18 0.59 0.1 4.21 0.54 (m)
dind15 ~~ dind15 1 1 2.90 -0.10 -0.35 0.1 2.91 0.40 (i)
aind15 ~~ aind15 3 3 2.90 0.10 0.42 0.1 2.87 0.40 (i)
aind13 ~~ aind13 1 1 2.61 0.08 0.53 0.1 3.64 0.48 (i)

Vertical Individualism

group_strict_loadings
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W4 =~ dind7 4 4 3.5 0.19 0.13 0.1 1.02 0.17 (i)
group_strict_intercepts
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W1 ~1 2 2 7.79 -0.32 -0.32 0.1 0.76 0.14 (m)
aind6 ~1 2 2 4.71 -0.13 -0.12 0.1 2.74 0.38 (m)
vrt_ind_W1 ~1 1 1 4.30 0.18 0.18 0.1 1.34 0.21 (m)
bind5 ~1 1 1 3.34 0.08 0.09 0.1 5.15 0.62 (i)
cind5 ~1 2 2 3.11 -0.15 -0.16 0.1 1.40 0.22 (i)
group_strict_variances
lhs op rhs block group mi epc sepc.all delta ncp power decision
vrt_ind_W1 ~~ vrt_ind_W1 1 1 3.55 0.28 1.00 0.1 0.46 0.10 (i)
vrt_ind_W1 ~~ vrt_ind_W1 4 4 3.17 -0.30 -1.00 0.1 0.35 0.09 (i)
aind5 ~~ aind5 3 3 2.93 0.09 0.77 0.1 3.73 0.49 (i)